The closed graph theorem for multilinear mappings.
The closed neighborhood and filter conditions in solid sequence spaces.
The closure of the invertibles in a von Neumann algebra
In this paper we consider a subset  of a Banach algebra A (containing all elements of A which have a generalized inverse) and characterize membership in the closure of the invertibles for the elements of Â. Thus our result yields a characterization of the closure of the invertible group for all those Banach algebras A which satisfy  = A. In particular, we prove that  = A when A is a von Neumann algebra. We also derive from our characterization new proofs of previously known results, namely Feldman...
The coercitivity of elliptic sesquilinear forms on the Sobolev spaces [Abstract of thesis]
The cofinal property of the reflexive indecomposable Banach spaces
It is shown that every separable reflexive Banach space is a quotient of a reflexive hereditarily indecomposable space, which yields that every separable reflexive Banach is isomorphic to a subspace of a reflexive indecomposable space. Furthermore, every separable reflexive Banach space is a quotient of a reflexive complementably -saturated space with and of a saturated space.
The cohomology of the diffeomorphism group of a manifold is a Gelfand-Fuks cohomology
The cohomology ring of free loop spaces.
The commutators of analysis and interpolation
The boundedness properties of commutators for operators are of central importance in Mathematical Analysis, and some of these commutators arise in a natural way from interpolation theory. Our aim is to present a general abstract method to prove the boundedness of the commutator for linear operators and certain unbounded operators that appear in interpolation theory, previously known and a priori unrelated for both real and complex interpolation methods, and also to show how the abstract result...
The Compact Approximation Property does not imply the Approximation Property
It is shown how to construct, given a Banach space which does not have the approximation property, another Banach space which does not have the approximation property but which does have the compact approximation property.
The compact endomorphisms of the metric linear spaces
The compact weak topology on a Banach space.
Throughout [this paper], E and F will denote Banach spaces. The bounded weak topology on a Banach space E, noted bw(E) or simply bw, is defined as the finest topology that agrees with the weak topology on bounded sets. It is proved in [3] that bw(E) is a locally convex topology if and only if E is reflexive.In this paper we introduce the compact weak topology on a Banach space E, noted kw(E) or simply kw, as the finest topology that agrees with the weak topology on weakly compact subsets. Equivalently,...
The ...-Compact-Open Topology and its Relatives.
The compactum and finite dimensionality in Banach algebras.
The compactum of a semi-simple commutative Banach algebra.
The complemented subspace problem revisited
We show that if X is an infinite-dimensional Banach space in which every finite-dimensional subspace is λ-complemented with λ ≤ 2 then X is (1 + C√(λ-1))-isomorphic to a Hilbert space, where C is an absolute constant; this estimate (up to the constant C) is best possible. This answers a question of Kadets and Mityagin from 1973. We also investigate the finite-dimensional versions of the theorem.
The completely continuous property in Orlicz spaces.
We show that in Orlicz spaces equipped with Luxemburg norm and Orlicz norm, the RNP, CCP, PCP and CPCP are equivalent.
The complex Grothendieck inequality for 2x2 matrices
The Complex Stone-Weierstrass Property
The compact Hausdorff space X has the CSWP iff every subalgebra of C(X,ℂ) which separates points and contains the constant functions is dense in C(X,ℂ). Results of W. Rudin (1956) and Hoffman and Singer (1960) show that all scattered X have the CSWP and many non-scattered X fail the CSWP, but it was left open whether having the CSWP is just equivalent to being scattered. Here, we prove some general facts about the CSWP; in particular we show that if X is a compact ordered space,...
The Components of a Positive Operator.
The concentration-compactness principle in the calculus of variations. The locally compact case, part 2